1 Determinearewhether the following polynomialson the adjacent fields.irreduciblea) f(x)= x³ +5x² + 2x+16b)22x4-9x³+ 16x²p(x) =+18 x + 20+18x+20, 9

Answered: 11 Determine are whether the following…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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6. List all polynomials of the form x++bx+cx²+dx+e with rational coefficients that are factors of the polynomial, x¹²-1.
5 Write the following polynomials as coefficient vectors: 2x3-3x2 + x + 5 I 3x5+ x2-4
Which of the following sets of polynomials span R² O A and B OC= {2-3t, 5t+t², −3+ 4t+2t², 1-8t - 2t²} OB and C OB={1-², 1-3t+5t², -3+5t-7t², -4+5t - 6t²} O A = {1,1,²} A and C OA, B and C
Show that the given values for a and b are lower and upper bounds for the real zeros of the polynomial. P(x) = 2x3 + 9x2 + 3x – 4; a = -5, b = 1 for a = -5: -5[ 2 9. 3 -4 Since the row containing the quotient and remainder has ---Select-- a = -5 is | ---Select--- for b = 1: 1 2 Since the row containing the quotient and remainder has --Select--- b = 1 is -Select---
2. Which polynomial expresses the difference of the two polynomials below? (-8k* + 3k³ – 6) – (9k* – 11k + 2) A. –17k4 + 14k³ 3 4 - B. –17k4 + 14k³ – 8 3 O C. –17k4 – 8k³ – 8 O D. –17k4 – 8k³ – 4 -
Write the polynomial as the product of linear and quadratic factors that are irreducible over the reals. Ax) = x* + 42x2 – 343 o (x? + 49)(x + 7)(x – 7) | (x² + 49)[x + /7)(x + /7) o (x? + 49)(x - V7)(x - 7) (x² + 49)(x + 7)(x - /7) (x² + 49)[x + /7][x - /7)
#21
What are the possible integer zeros of each polynomial function? a) a) P(n) = n ^ 3 - 2n ^ 2 - 5n + 12 b) P(p) = p ^ 4 - 3p ^ 3 - p ^ 2 + 7p - 6 c) P(z) = z ^ 4 + 4z ^ 3 + 3z ^ 2 + 8z - 25 d) P(y) = y ^ 4 - 11y ^ 3 - 2y ^ 2 + 2y + 10
Write each of the following polynomials as a product of irreducibles in Q[r]. (a) a4 – 10r3 + 35x? – 48x + 18 (b) x4 + 2x3 + x² + 3x + 2
Show that (n+lp to %3D Use the legender Polynomials %3D elhem Press

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11 Determine are whether the following polynomials the adjacent fields. irreducible p(x) = on a) f(x)= x³ +5x² + 2x+16 b) 22x4-9x3+ 16x² +18x+20 +18x+20, 9